See how 4 dimensional quaternions involve vectors in 3-space and how the quaternion function F(v) = nvn gives a simple algebraic method of working with reflections in planes in 3-space.
An account of multiplication of vectors, both scalar products and vector products.
Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.
Form a sequence of vectors by multiplying each vector (using vector products) by a constant vector to get the next one in the seuence(like a GP). What happens?
Explore the meaning of the scalar and vector cross products and see how the two are related.